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A301647 a(n) = n^3 - (n mod 2). 0
0, 8, 26, 64, 124, 216, 342, 512, 728, 1000, 1330, 1728, 2196, 2744, 3374, 4096, 4912, 5832, 6858, 8000, 9260, 10648, 12166, 13824, 15624, 17576, 19682, 21952, 24388, 27000, 29790, 32768, 35936, 39304, 42874, 46656, 50652, 54872, 59318, 64000, 68920, 74088, 79506, 85184, 91124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) is the circumference of the n X n X n grid graph for n > 1.

LINKS

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Graph Circumference

Eric Weisstein's World of Mathematics, Grid Graph

Index entries for linear recurrences with constant coefficients, signature (3, -2, -2, 3, -1).

FORMULA

a(n) = (2 n^3 + (-1)^n - 1)/2.

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5).

G.f.: 2*x^2*(4 + x + x^2)/((-1 + x)^4*(1 + x)).

MAPLE

seq(n^3-modp(n, 2), n=1..50); # Muniru A Asiru, Mar 25 2018

MATHEMATICA

Table[n^3 - Mod[n, 2], {n, 20}]

Table[(2 n^3 + (-1)^n - 1)/2, {n, 20}]

LinearRecurrence[{3, -2, -2, 3, -1}, {0, 8, 26, 64, 124}, 20]

CoefficientList[Series[2 x (4 + x + x^2)/((-1 + x)^4 (1 + x)), {x, 0, 20}], x]

PROG

(GAP) List([1..50], n->n^3- n mod 2); # Muniru A Asiru, Mar 25 2018

(PARI) a(n) = n^3 - (n%2); \\ Altug Alkan, Mar 25 2018

CROSSREFS

Cf. A137932 (circumference of n X n grid graph).

Sequence in context: A211640 A002901 A213769 * A050471 A088024 A296112

Adjacent sequences:  A301644 A301645 A301646 * A301648 A301649 A301650

KEYWORD

nonn,easy

AUTHOR

Eric W. Weisstein, Mar 25 2018

STATUS

approved

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Last modified November 11 22:31 EST 2019. Contains 329046 sequences. (Running on oeis4.)